Based on the decision-makers' utility function, the attributes value matrix is converted to the subjective attributes value matrix to reflect their subjective judgments on the attributes value. By utilizing the entropy weighting technique, the decision-maker's subjective weight and objective weight of attributes are determined individually based on the subjective attributes value matrix and attributes value matrix. Then, based on the principle of minimum cross-entropy, all decision-makers' subjective weights are integrated into a single weight vector. Then, by applying the principle of minimum cross-entropy again, a weight aggregation method is proposed to combine the subjective and objective weight of attributes. Finally, a multiple attribute group decision-making(MAGDM) example of project choosing is presented to illustrate the procedure of the proposed method. The method proposed fully takes all decision-makers'various evaluation on a multiple attribute decision-making(MADM) problem into consideration, which provides a feasible method based on the information-theoretic entropy to aggregate weights in MAGDM problems.